Single vortex states in a confined Bose-Einstein condensate

It has been demonstrated experimentally that non-axially symmetric vortices precess around the centre of a Bose-Einstein condensate. Two types of single vortex states have been observed, usually referred to as the S-vortex and the U-vortex. We study theoretically the single vortex excitations in spherical and elongated condensates as a function of the interaction strength. We solve numerically the Gross-Pitaevskii equation and calculate the angular momentum as a function of precession frequency. The existence of two types of vortices means that we have two different precession frequencies for each angular momentum value. As the interaction strength increases the vortex lines bend and the precession frequencies shift to lower values. We establish that for given angular momentum the S-vortex has higher energy than the U-vortex in a rotating elongated condensate. We show that the S-vortex is related to the solitonic vortex which is a nonlinear excitation in the nonrotating system. For small interaction strengths the S-vortex is related to the dark soliton. In the dilute limit a lowest Landau level calculation provides an analytic description of these vortex modes in terms of the harmonic oscillator states

Enhancement of the scissors mode of an expanding Bose-Einstein condensate

We study the time-evolution of the scissors mode of a Bose-Einstein condensate during the ballistic expansion after release from the magnetic trap. We show that despite the nontrivial character of the superfluid expansion, the sinusoidal behavior of the scissor oscillations is recovered after an asymptotic expansion, with an enhancement of the final amplitude. We investigate this phenomenon with a condensate held in an elongated magnetostatic potential, whose particular shape allows for the excitation of the scissors mode.Comment: RevTeX, 5 figure

Unstable regimes for a Bose-Einstein condensate in an optical lattice

We report on the experimental characterization of energetic and dynamical instability, two mechanisms responsible for the breakdown of Bloch waves in a Bose-Einstein condensate interacting with a 1D optical lattice. A clear separation of these two regimes is obtained performing measurements at different temperatures of the atomic sample. The timescales of the two processes have been determined by measuring the losses induced in the condensate. A simple phenomenological model is introduced for energetic instability while a full comparison is made between the experiment and the 3D Gross-Pitaevskii theory that accounts for dynamical instability

ZMP Constraint Restriction for Robust Gait Generation in Humanoids

We present an extension of our previously proposed IS-MPC method for humanoid gait generation aimed at obtaining robust performance in the presence of disturbances. The considered disturbance signals vary in a range of known amplitude around a mid-range value that can change at each sampling time, but whose current value is assumed to be available. The method consists in modifying the stability constraint that is at the core of IS-MPC by incorporating the current mid-range disturbance, and performing an appropriate restriction of the ZMP constraint in the control horizon on the basis of the range amplitude of the disturbance. We derive explicit conditions for recursive feasibility and internal stability of the IS-MPC method with constraint modification. Finally, we illustrate its superior performance with respect to the nominal version by performing dynamic simulations on the NAO robot

Maximally localized Wannier functions for ultracold atoms in one-dimensional double-well periodic potentials

We discuss a method for constructing generalized Wannier functions that are maximally localized at the minima of a one-dimensional periodic potential with a double-well per unit cell. By following the approach of (Marzari M and Vanderbilt D 1997 Phys. Rev. B 56, 12847), we consider a set of band-mixing Wannier functions with minimal spread, and design a specific two-step gauge transformation of the Bloch functions for a composite two band system. This method is suited to efficiently compute the tight-binding coefficients needed for mapping the continuous system to a discrete lattice model. Their behaviour is analyzed here as a function of the symmetry properties of the double-well (including the possibility of parity-breaking), in a range of feasible experimental parameters.Comment: 21 pages, 10 figures; revised version; corrected Figs. 2 and 8; added reference

Anharmonic parametric excitation in optical lattices

We study both experimentally and theoretically the losses induced by parametric excitation in far-off-resonance optical lattices. The atoms confined in a 1D sinusoidal lattice present an excitation spectrum and dynamics substantially different from those expected for a harmonic potential. We develop a model based on the actual atomic Hamiltonian in the lattice and we introduce semiempirically a broadening of the width of lattice energy bands which can physically arise from inhomogeneities and fluctuations of the lattice, and also from atomic collisions. The position and strength of the parametric resonances and the evolution of the number of trapped atoms are satisfactorily described by our model.Comment: 7 pages, 5 figure

A multiband envelope function model for quantum transport in a tunneling diode

We present a simple model for electron transport in semiconductor devices that exhibit tunneling between the conduction and valence bands. The model is derived within the usual Bloch-Wannier formalism by a k-expansion, and is formulated in terms of a set of coupled equations for the electron envelope functions. Its connection with other models present in literature is discussed. As an application we consider the case of a Resonant Interband Tunneling Diode, demonstrating the ability of the model to reproduce the expected behaviour of the current as a function of the applied voltageComment: 8 pages, 4 figure

Dilute Bose gas with correlated disorder: A Path Integral Monte Carlo study

We investigate the thermodynamic properties of a dilute Bose gas in a correlated random potential using exact path integral Monte Carlo methods. The study is carried out in continuous space and disorder is produced in the simulations by a 3D speckle pattern with tunable intensity and correlation length. We calculate the shift of the superfluid transition temperature due to disorder and we highlight the role of quantum localization by comparing the critical chemical potential with the classical percolation threshold. The equation of state of the gas is determined in the regime of strong disorder, where superfluidity is suppressed and the normal phase exists down to very low temperatures. We find a $T^2$ dependence of the energy in agreement with the expected behavior in the Bose glass phase. We also discuss the major role played by the disorder correlation length and we make contact with a Hartree-Fock mean-field approach that holds valid if the correlation length is very large. The density profiles are analyzed as a function of temperature and interaction strength. Effects of localization and the depletion of the order parameter are emphasized in the comparison between local condensate and total density. At very low temperature we find that the energy and the particle distribution of the gas are very well described by the T=0 Gross-Pitaevskii theory even in the regime of very strong disorder.Comment: 27 pages, 20 figure

Anderson localization of elementary excitations in a one dimensional Bose-Einstein condensate

We study the elementary excitations of a transversely confined Bose-Einstein condensate in presence of a weak axial random potential. We determine the localization length (i) in the hydrodynamical low energy regime, for a domain of linear densities ranging from the Tonks-Girardeau to the transverse Thomas-Fermi regime, in the case of a white noise potential and (ii) for all the range of energies, in the ``one-dimensional mean field regime'', in the case where the randomness is induced by a series of randomly placed point-like impurities. We discuss our results in view of recent experiments in elongated BEC systems.Comment: 11 pages, 6 figures. Final printed versio